Mathematically funny

How to use Game Theory to Lose Weight

November 25, 2016

Just the other day, I was showing my blog to Dr Lakshmanan. He is a senior faculty at our college, and had introduced me to Theory of Computation (one of my favourite subjects). Anyway, he skipped the post on Good Math Bad Math (which I take pride in), and started reading the blogpost on Fruit Bread (which I obviously don’t). He went through it, and asked me, “So Surya, how are you still not that fat?”

“Sir, my roommate and I have a strategy.” And then I explained it to him. After listening carefully to our strategy, he smiled and said, “So you are basically using Game Theory to lose weight.”

Before I start telling you what exactly we do, I’ll explain what a Two-Person-Zero-Sum game is. It’s basically a part of game theory.

You may have noticed this yourself. Ever seen ATMs of different banks built side by side?

Did you wonder, “Why have two at the same place? Why not just space it out?”

This is because they are essentially competitors and one bank’s gain is the other bank’s loss. That is the essence of a two-person-zero-sum game. Consider a situation in which each of two banks want to set up an ATM on the same street. Assume that people on the street will always go to the closest ATM.

In year 1, HDFC, marked in green, and SBI, marked in yellow, decide to be friends, “Okay, we are competitors. We should divide this street between ourselves.” It was just like communism: the idea sounded pretty nice in theory.

It’s now Year 2, and HDFC bosses are furious that they aren’t getting enough customers. So they shift their ATM inside SBI’s territory, and there’s nothing SBI can do about it. SBI naturally gets upset and starts a fight (except during lunch time).

So Year 3, they decide that alright, enough is enough. Let’s set up shop at the centre of the street so that nobody can eat away at the other’s profit. They are now at Nash Equilibrium where neither can make a profit unless the other one budges. This is the same reason why you may see MacDonald’s and KFCs, Bharat Petroleums and Indian Oils next to each other.

That, ladies and gentlemen, is also how Varun and I unwittingly modelled our strategy to lose weight.

Story time.

It’s the night before an exam on Computer Networks, so of course we have a lot of time to waste on other things. I look at my roommate Varun, and ask, “Bro, why are we gaining so much of weight?”

“Because we can’t help ourselves when we see junk food?”

That got me thinking. What is the only thing more lucrative than food?

The answer was obvious: money!

I turned to the last page of the notebook open in front of me. I wrote down all the common junk food we eat.

And then, I assigned each of them a fine amount. After a deliberation of over half an hour, Varun and I agreed to abide by the condition that whenever one of us eats something from the list, the corresponding fine must be paid to the other guy. One person’s loss to become the other person’s gain.

It was awfully difficult at first. Imagine walking past Amul and seeing Rs20 fines in the place of the frozen yogurts. But slowly we got used to it. It was game theory being applied in real life! There were moments when we knew that if both of us bought the same junk food, we’d not have to pay a fine. But if just one of us backed out, the other would’ve had to pay a fine. And there’s absolutely no greater shame than having to pay a fine to a friend.

Till date, neither of us has paid a fine. We are at the Nash Equilibrium where neither makes a profit unless the other one incurs a loss. It is in our mutual interest to do so, and in the process, we have drastically cut down on our in-take of junk food.

In a situation where lectures from parents, and scary news reports failed, a simple application of Game Theory worked!

If you want to check out the blogpost on Fruit Bread, click here. For the blogpost on Good Math Bad Math, click here.

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